Circles

1103021612

Level: 
B
Consider two circles: the circle k with centre S1 and radius 3cm, and the circle n with centre S2 and radius 8cm. The distance between S1 and S2 is 22cm. Common internal tangents of the circles intersect at point A. Calculate the distance of the point A from the centre S1. (See the picture.)
6cm
16cm
11cm
5cm

1103021613

Level: 
B
A circle is inscribed in a rhombus ABCD. The touching points of the circle and the rhombus divide each side into two parts that are 12dm and 25dm long. (See the picture.) Find the measure of the angle CAB. Round the result to two decimal places.
34.72∘
43.85∘
46.15∘
23.14∘

1103077103

Level: 
B
The length of the shortest diagonal in a regular polygon is 8cm. The measure of the angle between this diagonal and the side of the polygon is 20∘. Calculate the radius of a circle circumscribed about this polygon. Round the result to two decimal places.
6.22cm
5.22cm
4.26cm
11.69cm

1103077106

Level: 
B
Let an equilateral triangle have a side of length of 10cm. Suppose there is a circular sector inside the triangle that has the centre at one of the vertices of the triangle, and the arc touches the opposite side (see the picture). Calculate the length of the arc of the sector. Round the result to two decimal places.
9.07cm
8.62cm
8.93cm
9.05cm

1103077107

Level: 
B
The figure shows an equilateral triangle whose side is 10cm long. The circular sector inside the triangle has the centre at one of the vertices of the triangle, and the arc touches the opposite side. Find the ratio of the circumference of the sector to the perimeter of the triangle. Round the result to one decimal place.
0.9
0.5
0.8
1.5

1103077108

Level: 
B
The figure shows an equilateral triangle whose side is 10cm long. The circular sector inside the triangle has the centre at one of the vertices of the triangle, and the arc touches the opposite side. Calculate the area of the sector. Round the result to one decimal place.
39.3cm2
37.5cm2
14.4cm2
3.75cm2